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A negative solution of Kuznetsov's problem for varieties of bi-Heyting algebras (2104.05961v1)
Published 13 Apr 2021 in math.LO
Abstract: We show that there exist (continuum many) varieties of bi-Heyting algebras that are not generated by their complete members. It follows that there exist (continuum many) extensions of the Heyting-Brouwer logic $\mathsf{HB}$ that are topologically incomplete. This result provides further insight into the long-standing open problem of Kuznetsov by yielding a negative solution of the reformulation of the problem from intermediate logics to extensions of $\mathsf{HB}$.
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